The induction of gene expression by synaptic activity is essential for the later phases of long-term synaptic potentiation and depression (LTP & LTD). While activity-dependent transcriptional events in neurons appear to be necessary for memory consolidation, there is poor understanding of the specific target genes and the molecular interactions between transcription factors and the promoter regions of these target genes that are required for the later phases of synaptic plasticity. The field has been hampered by a series of technical limitations in this endeavor. These include an inability to record the gene expression-dependent late phase of synaptic plasticity in single mammalian neurons and to study late phase synaptic plasticity using precise activation of individual, defined and imaged synapses. Furthermore, it has not been straightforward to mutate and engineer defined promoter regions of candidate plasticity genes and to image the expression of target genes in individual neurons undergoing synaptic LTP/LTD. We have solved these technical limitations and so can perform long-term patch-clamp recording of the transcription-dependent late phase of cerebellar LTD in single Purkinje cells in cultures and brain slices, evoked by uncaging of glutamate at defined dendritic spines, while imaging spine and nuclear Ca and fluorescent markers of gene expression. We perform these experiments in neurons from null mice and transfected with engineered bacterial artificial chromosomes (BACs) to easily manipulate the promoters of relevant genes. This work has revealed that the late phase of LTD requires transcription of the Arc gene. We hypothesize that climbing fiber activation drives nuclear Ca and CREB binding to Arc CRE6.9 and that climbing fiber + parallel fiber co-activation is necessary to initiate phosphatase and MAL signaling cascades that originate in activated parallel fiber spines and propagate to the nucleus to result in MEF2D and SRF binding to MRE6.9 and SRE6.9 in the Arc promoter respectively. In this way, all three binding events in the SARE region of the Arc promoter are necessary to trigger Arc transcription and the late phase of LTD. If our hypothesis is correct, this would be a double-AND logical operator encoded in the structure of the Arc promoter. Associativity is the hallmark of many memory traces, yet remains almost entirely unexplored for late phases of LTP/LTD in any brain region or model organism.